# Experimental design for discrete choice response

I'm designing a survey where people need to choose one of three transportation alternatives. Here are the alternatives, their specific factors/attributes and the levels I intend to use for each:

Regular car:
Fixed cost: 3 levels: $$10.00,$$15.00, $$20.00 Variable cost: 3 levels:$$0.25, $$0.50,$$0.75
No waiting time
Electric car:
Fixed cost: 3 levels: $$05.00,$$15.00, $$30.00 Variable cost: 3 levels:$$0.25, $$0.50,$$0.75
No waiting time
Taxi:
No fixed cost
Variable cost: 3 levels: $$2.00,$$3.00, $4.00 Waiting time: 3 levels: 2min, 5min, 8min  Besides all of this, there is another factor/attribute that should be taken into account in the design which doesn't "belong" to any of the alternatives - it's a factor that affects people's choices "externally". It would be something like this: Weather condition: 3 levels: sunny, rainy and overcast  Notice how I would have ONE weather condition per choice occasion, not one weather condition per alternative. I've created designs with about 40 or 50 runs, but I can't possibly ask every person in my survey to answer 50 versions of a very similar question. In my case, I would like each respondent to receive only 2 choice occasions (i.e. 2 "repetitions" per survey). So, for example, one survey would look something like this: Question 1 When the weather is sunny, which one of these modes would you use? Regular car: FC=\$10.00, VC=\$0.75, WT=0min Electric car: FC=\$30.00, VC=\$0.50, WT=0min Taxi: FC=\$00.00, VC=\$3.00, WT=5min Question 2 When the weather is rainy, which one of these modes would you use? Regular car: FC=\$15.00, VC=\$0.50, WT=0min Electric car: FC=\$05.00, VC=\$0.75, WT=0min Taxi: FC=\$00.00, VC=\\$4.00, WT=2min

(FC = Fixed cost, VC = Variable cost, WT = Waiting time)

Since this will be a paper-based survey (yes, old school printing, mail-out and all that), it would make logistics MUCH easier if I only have around 10 versions of the survey.

Does anyone know what software to use for this kind of design?

I have found how to generate orthogonal designs and fractional factorial designs in R and SPSS. However, I haven't found how to split those designs into groups of 2 questions and still guarantee a small number of overall versions of the survey.

I also found that some design of experiment tools (such as JMP's "Choice DoE" module) were made considering that all of the alternatives share exactly the same attributes and levels. In other words, the alternatives themselves are almost identical to each other, and the only thing that sets them apart from one another are the attribute levels, making the alternatives almost perfect substitutes (e.g. hard drives with different capacities, write speeds and costs; or potato chips with different flavors, textures and costs).

I can clearly recognize that the situation I'm dealing with is different: even if costs and travel times are the same, there is still some fundamental difference between regular cars, electric cars and taxis that might make people choose one over the other. Since this is the case, I'm not sure the default tools I found are appropriate for developing a DoE for this problem.

Does anyone know any resources I could look at to help with this? I've already taken a look at Hensher, Rose & Greene's "Applied Choice Analysis" and Louviere, Hensher & Swait's "Stated Choice Methods", but the language seems incredibly cryptic and dense.

TL;DR
What tools would you use to design an experiment where you have the following particularities:
- The outcome to be analyzed is a discrete-choice outcome
- Not all alternatives share the same attributes and/or attribute levels
- Some attributes analyzed affect all alternatives simultaneously
- You want to ensure a reasonable amount of repetitions/choice occasions per respondent (around 2 or 3) such that you don't fatigue the respondent
- All versions of the survey have to be created beforehand (i.e. cannot randomly choose from a full design for each respondent) due to printing and other logistical constraints

• Kuhfeld has a pretty comprehensive guide on this: support.sas.com/techsup/technote/mr2010.pdf, see page 285-663. It also talks about alternatives that do not need to compile all permutations, provided that your can compromise on the analysis scheme. – Penguin_Knight Aug 24 '18 at 21:22
• Awesome, thanks! I'll take a look and see if it makes these things clearer. – Felipe D. Aug 27 '18 at 16:09